Log Gaussian Cox processes on the sphere

We define and study the existence of log Gaussian Cox processes (LGCPs)
for the description of inhomogeneous and aggregated/clustered point patterns
on the d-dimensional sphere, with d = 2 of primary interest. Useful theoretical
properties of LGCPs are studied and applied for the description of sky
positions of galaxies, in comparison with previous analysis using a Thomas
process. We focus on simple estimation procedures and model checking based
on functional summary statistics and the global envelope test.